Let P_X = X $X ^ { \prime }$ X)^-1

question 49

Multiple Choice

Let P_X = X( $X ^ { \prime }$ X) ^-1 $X ^ { \prime }$ and M_X = I_n - P_X. Then M_X M_X =

• A)X( \(X ^ { \prime }\) X)^-1 \(X ^ { \prime }\) - P_X.
• B) \(M _ { X } ^ { 2 }\)
• C)I_n.
• D)M_X.

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Definitions:

Gene Family

A group of genes sharing a common origin that typically encode proteins with similar functions.

Molecular Clock

A method used to determine time based on base pair substitutions. Molecular clocks use the rates of molecular change to deduce the divergence time between lineages in a phylogeny, for example. They work best when they can be “calibrated” with other markers of time, such as fossils with known ages and placements.

Synapomorphy

A trait that is shared by two or more taxa and their most recent common ancestor, used to infer evolutionary relationships.

Phylogenetic Methods

Techniques used in biology to infer the evolutionary relationships and history among different species or genes.